Comparison on two ways of phonon spectral property reconstruction from thermal spectroscopy experiment

TL;DR

This paper investigates the reconstruction of phonon transport properties from thermal spectroscopy, revealing that the cumulative thermal conductivity function is not unique to the relaxation-times distribution, and emphasizes the importance of directly reconstructing the frequency-dependent relaxation-times.

Contribution

The study demonstrates that the cumulative thermal conductivity does not uniquely determine relaxation-times, and confirms that reconstructing the frequency-dependent relaxation-times yields numerically unique solutions.

Findings

$F(\Lambda)$ is not unique to relaxation-times distributions.

Reconstruction based on frequency-dependent relaxation-times is numerically unique.

Extensive optimization validates the proposed reconstruction method.

Abstract

We examine the reliability of the cumulative thermal conductivity as a function of the free path, $F(\Lambda)$, in the context of reconstruction of phonon transport properties from thermal spectroscopy experiments. We specifically show that a given $F(\Lambda)$ does not correspond to a unique relaxation-times function, in the sense that more than one distribution of relaxation-times can result in the same $F(\Lambda)$. Since different relaxation-time distributions will, in general, lead to different thermal responses, $F(\Lambda)$ does not uniquely predict the material thermal response in all transport regimes. This implies that in the context of thermal transport at the nanoscale within the Boltzmann relaxation-time approximation framework, the fundamental property that should be reconstructed from the thermal spectroscopy experiments is the frequency-dependent relaxation-times function (provided group velocities are known), since it explicitly appears in the governing equation as the input material property. Extensive global optimization studies show that a previously proposed formulation for reconstruction based on the frequency-dependent relaxation-times function [Physical Review B 94, 155439 (2016)] provides numerically unique solutions.